2.1 All, Every, No and None Statements
Key Takeaways
- All A are B places A inside B but does not prove that all B are A.
- No A are B excludes overlap and can be restated symmetrically as no B are A.
- Diagrams and short set labels help preserve direction when a passage contains several categories.
The official task
Critical Thinking contains five passages and 23 conclusions in 30 minutes. Each passage supplies a set of facts. For every proposed conclusion, decide True, False, or Indeterminable. The official guide begins its logic instruction with category words such as all, every, no, none, and some because a small change in scope can reverse an answer.
Treat the passage as a closed fact set. A label such as courier, inspector, or officer is only a category symbol unless the passage defines more. Real-world knowledge about those jobs must not fill a missing relationship.
All and every: one-way inclusion
Translate All A are B as A → B or as a small A circle completely inside a larger B circle. Every member of A belongs to B. The statement does not say that every B belongs to A.
Example facts:
- All credential reviewers are trained employees.
- All trained employees completed orientation.
Necessary conclusions:
- Every credential reviewer completed orientation.
- Some people who completed orientation may be credential reviewers if the passage establishes that reviewers exist.
Unsupported converse:
- All employees who completed orientation are credential reviewers.
The two arrows can be chained in their stated direction: reviewer → trained → orientation. They cannot be reversed. A common distractor begins with the larger category and claims membership in the smaller one.
The word only deserves special care. "Only registered guests enter Room R" means anyone who enters Room R is a registered guest: Room R entrant → registered. It does not mean every registered guest enters Room R. Rephrase an only statement before comparing it with a conclusion.
No and none: complete separation
Translate No A are B as two circles with no overlap. Unlike an all statement, the exclusion reads naturally in both directions:
- No temporary passes are permanent credentials.
- Therefore, no permanent credentials are temporary passes.
If a person or object is proved to be A, it cannot be B. If it is proved to be B, it cannot be A. But absence from A does not establish membership in B; there may be many other categories.
Example facts:
- No vehicles in Lot C are delivery vehicles.
- Van 8 is in Lot C.
The conclusion "Van 8 is not a delivery vehicle" is True. The conclusion "Van 8 is a staff vehicle" is Indeterminable because the facts exclude one category without naming the correct alternative.
Combining inclusion and exclusion
Universal statements often form a short chain:
- All night-shift supervisors are badge holders.
- No badge holders are escorted visitors.
- Rivera is a night-shift supervisor.
From these facts, Rivera is a badge holder and Rivera is not an escorted visitor. A conclusion that Rivera is an employee may sound plausible but remains Indeterminable if employee status is never stated.
Another pattern combines two groups inside a larger group:
- All inspectors are trained personnel.
- All schedulers are trained personnel.
This does not establish any relationship between inspectors and schedulers. They may overlap, may be separate, or may even be identical. Sharing a larger category never proves that two smaller categories overlap.
Diagram method
Use compact marks on scratch material when several groups appear:
- Write a one-letter or short label for each category.
- Draw an arrow for all/every.
- Draw a crossed link for no/none.
- Add named people only after mapping the rules.
- Test the proposed conclusion in the direction written.
For A → B → C and C × D, you may infer A → C and A × D. You may not infer C → A, and you know nothing about the relation between B and D beyond what follows through C.
Language traps
Watch for conclusions that quietly change scope:
- All becomes most or only.
- A rule about employees becomes a rule about every person at a location.
- A category relationship is reversed.
- Excluding one group is treated as proving a different group.
- A fact about one named individual is generalized to the whole category.
The safe question is: Could every passage fact remain true while this conclusion is false? If yes, the conclusion is not logically guaranteed. If the passage actively rules it out, it is False; if both possibilities remain open, it is Indeterminable.
Final direction check
Before committing to an answer, restate the relationship without the passage labels: "small group goes into large group" or "these groups cannot overlap." This quick translation exposes a reversed arrow before it costs a point.
Facts: All route coordinators are cleared employees. No cleared employees are escorted visitors. Lee is a route coordinator. Which conclusion must be true?